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The diffeomorphism type of certain $S^{3}$-bundles over $S^{4}$

Authors: Marc Sanchez and Frederick Wilhelm
Journal: Proc. Amer. Math. Soc. 130 (2002), 1139-1143
MSC (1991): Primary 53C20
Published electronically: November 9, 2001
MathSciNet review: 1873789
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Abstract: In this note we show that the unit tangent bundle of $S^{4}$ is diffeomorphic to the total space of a certain principal $S^{3}$-bundle over $S^{4}$, solving a problem of James and Whitehead.

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Additional Information

Marc Sanchez
Affiliation: 4243 Edgewood Place, Riverside, California 92506

Frederick Wilhelm
Affiliation: Department of Mathematics, University of California, Riverside, California 92521-0135

Keywords: Unit tangent bundle
Received by editor(s): March 20, 2000
Published electronically: November 9, 2001
Additional Notes: This work was partially suported by the NSF
Communicated by: Ralph Cohen
Article copyright: © Copyright 2001 American Mathematical Society